1. Check it out! 1 1.10.2: Proving Properties of Special Quadrilaterals

2. You are taking a road trip from Carrollton, Georgia, to Campton, Georgia, traveling through Atlanta. Your best efforts to avoid traffic will take you around the city of Atlanta, but you want to know how far it is “as the crow flies” (moving in a straight line) between Carrollton and Campton. 2 1.10.2: Proving Properties of Special Quadrilaterals

3. 1.When looking at a map with a grid, if Carrollton lies at (2, 2) and Campton lies at (10, 4.5), calculate the distance between those two cities if 1 unit on the grid is approximately 10 miles. 2.If Atlanta is the midpoint between the two cities, where does Atlanta lie on the grid? 3.What is the distance between Atlanta and each of the cities? 4.What is the slope of the line that passes through these three cities? 5.What is the slope of a line perpendicular to the line through the cities? 3 1.10.2: Proving Properties of Special Quadrilaterals

4. 1.When looking at a map with a grid, if Carrollton lies at (2, 2) and Campton lies at (10, 4.5), calculate the distance between those two cities if 1 unit on the grid is approximately 10 miles. Use the distance formula: 4 1.10.2: Proving Properties of Special Quadrilaterals

5. The distance between Carrollton and Campton is about 8.4 units. Multiply that by 10 miles. The distance between Carrollton and Campton is about 84 miles. 5 1.10.2: Proving Properties of Special Quadrilaterals

6. 2.If Atlanta is the midpoint between the two cities, where does Atlanta lie on the grid? Use the midpoint formula to find Atlanta’s location on the grid. Atlanta is at (6, 3.25) on the grid. 6 1.10.2: Proving Properties of Special Quadrilaterals

7. 3.What is the distance between Atlanta and each of the cities? By the definition of a midpoint, each shorter segment is half the distance of the total segment. Each city is about 42 miles from Atlanta. 7 1.10.2: Proving Properties of Special Quadrilaterals

8. 4.What is the slope of the line that passes through these three cities? Using the endpoints, calculate the slope of the line. The endpoints are the grid locations of Carrollton and Campton: (2, 2) and (10, 4.5). The slope is. 8 1.10.2: Proving Properties of Special Quadrilaterals

9. 5.What is the slope of a line perpendicular to the line through the cities? Perpendicular lines have opposite reciprocal slopes. Since the slope of the original line is, a line perpendicular to that line would have a slope of. 9 1.10.2: Proving Properties of Special Quadrilaterals